Incommensurate BiMO₃perovskites: Bi₂Mn_2/3M_2/3Ni_2/3O₆and Bi₂M′M′′O₆

Abstract

Artificial aperiodic structures, such as quasiregular heterostructures, photonic and phononic metamaterials, are an important and up-to-date research topic [1].The fabrication of such structures is mostly governed by algorithms based on substitution sequences [2],[3].The notions of "order" and "disorder" are context-dependent and subjective.For a deterministic structure "disorder" is a misnomer; the deviation from uniformity can be much better characterized and even quantified by symbolic complexity [2].We have studied double-sided and two-dimensional versions of various standard substitution sequences.Here we focus on the rectangle complexity [4] of a twodimensional version of the Prouhet-Thue-Morse sequence and set an upper bound for its entropy.We also briefly hint at the complexity and entropy of lattice animals (polyominoes) living on an aperiodic structure.